Answer:
The number of students who like none or only one of the foods is 20.
Explanation:
Consider the provided information.
First draw the Venn diagram as shown below:
25 like all three food and 40 like pizza and tacos .
40-25=15 likes only pizza and tacos.
25 like all three food and 37 like hoagies and tacos
37-25=12 likes only hoagies and tacos
25 like all three food and 28 like pizza and hoagies
28-25 = 3 like only pizza and hoagies .
Let P represents Pizza, H represents Hoagies and T represents Tacos.
Only Pizza = P - (only P and H + only P and T + All 3 foods)
Only Pizza = 48 - (3+ 15 + 25) = 5
Only Hoagies = H - (only P and H +only H and T - All 3 foods)
Only Hoagies = 45 - (3 + 12 + 25) = 5
Only Tacos = T - (only P and T + only H and T - All 3 food)
Only Tacos = 58 - (15 + 12 + 25) = 6
Total number of students are 75.
Total number of student who don't like any of the food is:
Total=P+H+T−(sum of 2 group overlaps)+(all three)+Neither
75=48+45+58−(28+37+40)+25+Neither
75=176−(105)+Neither
Neither = 4
The number of students who like none or only one of the foods = 4 + (5 + 5 + 6) = 20.
Hence, the required answer is 20.